Mathematics 10 — Exercise 7.3 · Q9

Full question

A listener is 6 m from each of two speakers, with a 30° angle between them. Find the distance between speakers.

Step-by-step solution

1. The listener and two speakers form a triangle with two sides 6 m and included angle 30°.

2. Use cosine law for the side between speakers.

   $$\mathrm{d²}=6^2+6^2-12\times 6\times \cos \left(\mathrm{30°}\right)$$

3. Square the sides and multiply 2×6×6=72.

4. Calculate this operation before combining the remaining terms.

   $$\left(-1\right)\times 36\times \sqrt{3}=\left(-36\right)\times \sqrt{3}$$

5. Substitute cos 30°=√3/2 and subtract from 72.

   $$72-36\times \sqrt{3}$$

6. Take the positive square root.

   $$3.1058285$$

Answer

The final answer is shown below.